Grade 12 Applied Mathematics Achievement Test. Student Booklet

Transcription

1 Grade 12 Applied Mathematics Achievement Test Student Booklet January 2017

2 Manitoba Education and Training Cataloguing in Publication Data Grade 12 applied mathematics achievement test. Student booklet. January 2017 This resource is available in print and electronic formats. ISBN: (print) ISBN: (pdf) 1. Educational tests and measurements Manitoba. 2. Mathematical ability Testing. 3. Mathematics Examinations, questions, etc. 4. Mathematics Study and teaching (Secondary) Manitoba. I. Manitoba. Manitoba Education and Training Manitoba Education and Training School Programs Division Winnipeg, Manitoba, Canada Permission is hereby given to reproduce this resource for non-profit educational purposes provided the source is cited. After the administration of this test, print copies of this resource will be available for purchase from the Manitoba Learning Resource Centre (formerly the Manitoba Text Book Bureau). Order online at This resource will also be available on the Manitoba Education and Training website at Websites are subject to change without notice. Disponible en français. While the department is committed to making its publications as accessible as possible, some parts of this document are not fully accessible at this time. Available in alternate formats upon request.

3 GRADE 12 APPLIED MATHEMATICS ACHIEVEMENT TEST DESCRIPTION Total Possible Marks: 61 Time: 3 hours Unit Description Marks A Relations and Functions 15 B Probability 15 C Financial Mathematics 17 D Design and Measurement 9 E Logical Reasoning 5 RESOURCES You may use the following resources: Formula Sheet (tear-out page at the back of this booklet) one 8½ 11 study sheet ruler graphing calculator, computer software, and/or app Internet access for tools such as applets or mortgage payment calculators Use of the Internet to communicate or access other content, including but not limited to course notes, definitions, or conceptual information is not permitted during the test. Electronic communication between students through phones, , or file sharing during the test is strictly prohibited. Applied Mathematics: Student Booklet (January 2017) 1

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5 DIRECTIONS Read all instructions on the test carefully. If you need extra paper or you print out an answer to a question, let the teacher know. Indicate in the response space of the question that your answer is on a separate sheet. Remember to indicate your input values by writing them in your booklet or printing a copy if using a technology tool include your booklet number and question number on additional pages (e.g., printouts) and attach them to the corresponding page in the booklet express your answers in decimal and percentage form to the nearest hundredth (two decimal places) when rounding, unless otherwise indicated Example: or 51.72% 29 = state any assumptions you make A graphic organizer is a visual representation of information. Examples include a tree diagram, a chart, a list, a Venn diagram, a truth table, Pascal s triangle, etc. A clearly communicated answer is easily identified in the response space includes the parameters in the equation, and y =, sin, ln, or x, as applicable includes the units of measure, where applicable includes labels, units, and scales for the axes on graphs is expressed as an exact value or is appropriately rounded Marks may be deducted for errors relating to any of the above. STOP PLEASE WAIT UNTIL INSTRUCTED TO TURN THE PAGE. Applied Mathematics: Student Booklet (January 2017) 3

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7 RELATIONS AND FUNCTIONS Question 1 Total: 1 mark Use the graph below to answer the following question and select the best answer The median of the graph is A. 2 B. 3 C. 5 D. 8 Applied Mathematics: Student Booklet (January 2017) 5

8 Question 2 Total: 2 marks Yang kicks a soccer ball off the ground. The height of the ball is tracked over time. The ball reaches a maximum height of 20 m at 2.1 seconds. 102 State the domain and range of the quadratic function that models the height of the soccer ball from when it is kicked until it hits the ground. Domain: Range: 6 Applied Mathematics: Student Booklet (January 2017)

9 Question 3 Total: 4 marks motor (generates waves) Stephanie experiments with the frequency of waves in a ripple tank during her Physics class. At the beginning of the experiment, she places a ruler into the tank and measures the median height of the water to be 10 cm. The water then rises to a maximum height of 13 cm at 1 second. (2 marks) a) Determine the sinusoidal regression equation that models the relationship between the height of the water and time. Show your work. 103 (1 mark) b) Determine the height of the water at 15 seconds. 104 (1 mark) c) Stephanie changes the settings of the motor to generate waves more quickly. Write an equation that can model this change if all other conditions remain the same. 105 Applied Mathematics: Student Booklet (January 2017) 7

10 Question 4 Total: 2 marks The average price of an electronic device is based on its memory capacity. The following equation models this relationship: P = ln c where P represents the average price in dollars and c represents the memory capacity in gigabytes (GB). (1 mark) a) What is the average price of a 256 GB device? 106 (1 mark) b) Provide one limitation of the equation that models this relationship Applied Mathematics: Student Booklet (January 2017)

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12 Question 5 Total: 6 marks Pam drives her car over a nail. As a result, one of the tires on her car starts to lose air pressure. Her tire pressure sensor provides the following data: t (h) P (psi) where P represents the air pressure (in psi) and t represents the time (in hours). (3 marks) a) Create a clearly labelled graph by plotting the given data. Draw a curve of best fit. 108 (1 mark) b) Determine the regression equation that best models the data in this situation Applied Mathematics: Student Booklet (January 2017)

13 c) The car becomes unsafe to drive when the tire pressure is 14 psi or under. How many hours can Pam safely drive her car after driving over the nail? 110 (2 marks) Express your final answer to the nearest hundredth (two decimal places). Show your work. Applied Mathematics: Student Booklet (January 2017) 11

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15 PROBABILITY Question 6 Total: 1 mark Select the best answer. 111 Which of the following expressions represents the number of ways to create a 4-digit passcode for your phone using the digits 0 to 9, if repetition is allowed? A B C. 10C 4 D. 10 P 4 Question 7 Total: 1 mark Select the best answer. 112 Scott can choose from 8 toppings to make a pizza. How many pizzas can be made with 3 different toppings? A. 6 B. 56 C. 336 D Applied Mathematics: Student Booklet (January 2017) 13

16 Question 8 Total: 3 marks Joseph has 20 cards; 4 cards of each of the following colours: red, blue, yellow, green, and purple. (1 mark) a) What is the probability of randomly drawing 2 red cards in a row if the first card is replaced before drawing the second card? 113 (1 mark) b) What is the probability of randomly drawing 2 red cards in a row if the first card is not replaced before drawing the second card? Applied Mathematics: Student Booklet (January 2017)

17 (1 mark) c) Explain which part, (a) or (b), is an example of dependent events. 115 Applied Mathematics: Student Booklet (January 2017) 15

18 Question 9 Total: 2 marks If 4 coins are tossed at the same time, what is the probability that they will land as either all heads or as all tails? Show your work Applied Mathematics: Student Booklet (January 2017)

19 Question 10 Total: 3 marks Last year, it was reported that 50.30% of Mathmatica s population was 40 years of age or older. 117 That same year, 65.74% of people 40 years of age or older saw a doctor and 60.09% of people younger than 40 years of age saw a doctor. If Mathmatica s population last year was , determine how many people in Mathmatica did not see a doctor. Show your work. Applied Mathematics: Student Booklet (January 2017) 17

20 Question 11 Total: 2 marks The probability that Louise will go out for dinner tonight is 0.4. The probability that she will watch a movie is 0.7. The probability she will do neither is 0.2. (1 mark) a) Draw a Venn diagram to represent this situation. 118 (1 mark) b) Determine the probability that Louise does only one of these activities Applied Mathematics: Student Booklet (January 2017)

21 Question 12 Total: 3 marks A coach randomly selects 5 players from a team of 18 to line up for a shot on goal. (1 mark) a) How many different 5-player arrangements are possible? 120 (2 marks) b) If Dustin and Andrew are 2 of the 18 players, what is the probability that Dustin will shoot first and Andrew will shoot second? Show your work. Express your answer as a fraction or round to the nearest thousandth (three decimal places). 121 Applied Mathematics: Student Booklet (January 2017) 19

22 FINANCIAL MATHEMATICS Question 13 Total: 1 mark Select the best answer. 122 Which of the following graphs shows the total amount of interest paid over the course of a 25-year mortgage? A. C. Interest (in thousands) Interest (in thousands) Years Years B. D. Interest (in thousands) Interest (in thousands) Years Years 20 Applied Mathematics: Student Booklet (January 2017)

23 Question 14 Total: 1 mark Select the best answer. 123 According to the Rule of 72, a reasonable estimate for the time it would take to double an investment of $ at an interest rate of 6.00%, compounded monthly is A. 3 years B. 4 years C. 12 years D. 18 years Applied Mathematics: Student Booklet (January 2017) 21

24 Question 15 Total: 4 marks Imani is going to buy a car. She can afford monthly payments of $ The dealer offers two financing options: 124 Option 1: financing over 60 months at a rate of 0.90% compounded monthly Option 2: financing over 60 months at a rate of 2.90% compounded monthly with an instant rebate of $ at the time of purchase Which option allows Imani to purchase a more expensive car? Show your work. 22 Applied Mathematics: Student Booklet (January 2017)

25 Question 16 Total: 2 marks Your friend has $ and is considering an investment in stocks, a guaranteed investment certificate (GIC), or rare collectibles. 125 Choose one of the three investments mentioned above and indicate one advantage and one disadvantage for your choice. Applied Mathematics: Student Booklet (January 2017) 23

26 Question 17 Total: 4 marks When she turned 25, Alexa began investing $ monthly into a mutual fund account producing average returns of 6.00%, compounded monthly. Alexa will stop contributing when she retires at age 55. (2 marks) a) How much money will her investment be worth at retirement? Show your work. 126 (2 marks) b) Alexa will withdraw $ per month from her account after retiring. If the average return rate stays the same, how old will she be when the account balance is zero? Show your work Applied Mathematics: Student Booklet (January 2017)

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28 Question 18 Total: 5 marks Shirley and Cameron have just moved to Brandon and are considering the two following housing options: Option 1: House for purchase purchase price of $ down payment of $ required 25-year mortgage at an interest rate of 3.00%, compounded semi-annually Option 2: Apartment for rent monthly payments of $ monthly parking fees of $60.00 (2 marks) a) What would be Shirley and Cameron s monthly mortgage payment with Option 1? Show your work Applied Mathematics: Student Booklet (January 2017)

29 (2 marks) b) What will be the total amount paid for each option at the end of 10 years? 129 (1 mark) c) State one advantage of renting the apartment. 130 Applied Mathematics: Student Booklet (January 2017) 27

30 DESIGN AND MEASUREMENT Question 19 Total: 2 marks Eleni is placing cups onto a 7 in. by 10 in. tray. Each cup has a circumference of 10 in. 131 Determine the maximum number of cups she can place on the tray. Show your work. 28 Applied Mathematics: Student Booklet (January 2017)

31 Question 20 Total: 4 marks You want to build a garden. The garden is square. (Diagram is not drawn to scale.) The side length is between 8 ft. and 10 ft. The garden is enclosed using boards stacked two boards high. There are 12 metal supports used to connect the structure. The garden is filled with soil to a depth of 15 in. Below is the price list for materials: 15 in. 132 Item metal supports boards soil Cost (plus GST and PST) $2.00 each $2.50/linear foot 3 $12.00/yd side length: ft. Determine the total cost of building your garden. All items must be purchased in whole units. Show your work. (Note: GST = 5%, PST = 8%) Applied Mathematics: Student Booklet (January 2017) 29

32 Question 21 Total: 3 marks (1 mark) a) What is the volume of a rubber hockey puck? (Diagram is not drawn to scale.) cm 7.62 cm (2 marks) b) How many pucks can be produced for $ if it costs $0.24 to print a logo on each puck and rubber costs $ per cm 3? Applied Mathematics: Student Booklet (January 2017)

33 LOGICAL REASONING Question 22 Total: 1 mark Select the best answer. 135 Given the following pattern: Which of the following continues this pattern? A. B. C. D. Applied Mathematics: Student Booklet (January 2017) 31

34 Question 23 Total: 2 marks You have 3 pails with volumes of 2 L, 3 L, and 5 L. 136 The 5 L pail is filled with water. The other pails are empty. 5 L 3 L 2 L Using only these pails, explain how to measure out exactly 4 L of water into the 5 L pail. 32 Applied Mathematics: Student Booklet (January 2017)

35 Question 24 Total: 2 marks Consider the original statement: If students are in Grade 12, then they will graduate this June. (1 mark) a) Write the converse of the statement. 137 (1 mark) b) Determine if a biconditional statement is possible. If yes, write the biconditional statement. If not, provide a counterexample. 138 END OF TEST Applied Mathematics: Student Booklet (January 2017) 33

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37 Formula Sheet: Applied Mathematics Relations and Functions y = ax + b 2 y = ax + bx + c 3 2 y = ax + bx + cx + d y = ab y = a + bln ( x) x y = alog b x y = asin( bx + c) + d y = a cos( bx + c) + d Probability ( or ) = ( ) + ( ) ( and ) P A B P A P B P A B ( and ) = ( ) ( ) P A B P A P B ( and ) = ( ) ( ) P A B P A P B A n n C P r r = n!! ( n r) n! = r! n r! ( ) Financial Mathematics t I 72 = i = Prt r A = P 1 + n Net worth = Total assets Total liabilities Debt-to-equity ratio (%) Gross debt service ratio (%) Rate of return (%) ( Total liabilities Mortgage) nt = 100 Net worth Monthly Monthly Monthly mortgage + property + heating payment taxes costs = 100 Gross monthly income Current value Previous value of portfolio of portfolio = 100 Previous value of portfolio Design and Measurement Prism: Surface area = Ph + 2B Volume = Bh Ps Pyramid: Surface area = B + ( s = slant height) 2 Bh Volume = 3 Sphere: Surface area = 4πr Volume = 4 πr Cylinder: Surface area = 2πrh + 2πr Applied Mathematics: Student Booklet (January 2017) 35 2 Volume = πrh Cone: Surface area = πr + πrs 2 πrh Volume = 3 2 2

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